WARNING! This is only a guide in order to focus your studying effort. The final will not be exactly like this. If it was, it would only be measuring your powers of memorization, and you know how I despise that. The problems presented here approximate those on the final; they do not mimic them. Please study over and above that which is given here.


circular motion & universal gravitation

centripetal force/acceleration characteristics. centripetal force relationships with velocity, mass, radius. apparent weight. Law of Universal Gravitation characteristics.

simple harmonic motion

period & frequency dependencies of pendulum and spring.


potential and kinetic states. conservation of mechanical energy. work – its relation to energy. power


impulse. momentum and its conservation. collision types.


wave characteristics and types. reflection. refraction. diffraction. interference. Doppler effect.


sound characteristics. decibel levels. beats/chords. resonance. harmonics/overtones.


1.  A mass of 1.5 kg moves in a circle of radius 25 cm at 2.0 rev/s. Calculate the required centripetal force for the motion.

2.  A car moving at 5.0 m/s tries to round a flat corner that has a radius of curvature of 8.0 m. How large must the coefficient of friction be between the wheels and the roadway for the car not to skid?

3. A pilot attempts a vertical loop during an air show. While upside-down at the top of the 245-meter radius loop he experiences a g-force of 2.75 g’s. Calculate the speed of the plane at this point.

4. How much would a German shepherd of mass 34.0 kg weigh on earth? How much would it weigh on Uranus? [massUr = 8.80 x 1025 kg radiusUr = 2.67 x 107 m]

5.  Calculate the frequency of an earth-bound pendulum of length 2.25 meters and mass 235 grams.

6. Two alien children from a distant planet are playing on their favorite toy, a Vinkel, which is essentially a vertical spring hooked to the ceiling with a seat attached to the other end. You sit on the seat and bounce up and down (this is not a very advanced civilization). Zorbert, who has a mass of 35.0 kg, bounces with a frequency of 0.550 Hz. When Annok (mass = 25.0 kg) rides on the same Vinkel, what is her period of oscillation?

7. A 60.0-kg woman walks up a flight of stairs that connects two floors 3.00 m apart. (a) How much lifting work is done? (b) By how much does the woman's gravitational potential energy change?

8. A 1200.-kg car sliding out of control along an icy (frictionless) road at 20.0 m/s travels up an equally icy hill. What is the greatest height reached by the car?

9. (referring to the last question) If the road and hill were not completely frictionless and the car reached a height of 15.0 m before coming to rest, how much work was done on the car by friction during its slide?

10. A 2.50-kg block slides down a frictionless incline, across a level frictionless floor and compresses an ideal spring. (k = 120. N/m) If the box originally began its journey from a height of 1.25 m above the floor, calculate (a) its speed at the bottom of the incline, (b) the maximum compression of the spring, and (c) the speed of the box when it is at a height of 0.350 m above the ground.

11. Calculate the average horsepower required to raise a 150.-kg drum to a height of 20.0 m in a time of 1.00 minute.

12. A 40000.-kg freight car is coasting at a speed of 5.00 m/s along a straight track when it strikes a 30000.-kg stationary freight car and couples to it. What will be their combined velocity after impact?

13. Two bodies of masses 8.00 kg and 4.00 kg move along the x-axis in opposite directions with velocities of +11.0 m/s and -7.00 m/s, respectively. They collide, and the 8.00-kg mass moves at + 1.00 m/s. (a) Find the velocity of the 4.00-kg mass. (b) Identify the type of collision.

14. A 2.00-kg block of wood rests on a tabletop. A 5.00-g bullet moving horizontally with a speed of 155 m/s is shot into the block, sticking in it. The block then slides along the table, stopping in 0.750 s. (a) Find the speed of the block just after impact, and (b) the frictional force between the block and the table.

15.  A hand grenade of mass 0.600 kg explodes into three pieces. a 0.400-kg piece moves at 155 m/s north and a 0.125-kg piece moves at 225 m/s west. Find the velocity of the third fragment.

16. Radio station WDVE in Pittsburgh broadcasts at a frequency of 102.5 MHz. The speed of radio waves is 3.00 x 108 m/s. What is the wavelength of WDVE's waves?

17. The wave shown below is being sent out by a 60-cycle/sec vibrating source. Find the wave’s

(a) amplitude, (b) frequency, (c) wavelength, and (d) speed.

18. A string 180 cm long resonates in three segments to transverse waves sent down it by a 270-Hz source. What is the speed of the waves on the string?

19. A locomotive moving at 30.0 m/s approaches and passes a person standing beside the track. Its whistle is emitting a note of frequency 2.00 kHz. What frequency will the person hear (a) as the train approaches and (b) as it recedes? (speed of sound = 340.0 m/s)

20. What is the speed of sound in air when the air temperature is 31.0°C?

21. What sound intensity is 40. dB louder than a 2.0 x 10-6 W/m² sound?

22. A certain organ pipe is tuned to emit a frequency of 196.0 Hz. When it and the G string of a violin are sounded together, 10.00 beats are heard in a time of 8.000 s. The violin string is slowly tightened, which causes its frequency to increase. As a result, the beat frequency decreases. What was the original frequency of the violin string?

23. A 256-Hz note and a 384-Hz note are played simultaneously. Identify the resulting chord as consonance or dissonance.

24. Determine the length of the shortest air column in a cylindrical jar that will strongly reinforce the sound of a 512-Hz tuning fork. (speed of sound = 340.0 m/s)

25. An organ pipe closed at one end is 61.0 cm long. What are the frequencies of the (a) 1st harmonic,

(b) 2nd overtone, and (c) 4th harmonic? (speed of sound = 340.0 m/s)

26. For a piano string of length 1.25 m, find the frequency of the (a) 2nd harmonic and the (b) 3rd overtone.

(speed of waves in string = 160. m/s)


1) 59 N

2) 0.31

3) 94.9 m/s

4) 333 N , 280. N

5) 0.332 Hz

6) 1.54 s

7) a. 1760 J b. 1760 J

8) 20.4 m

9) -63600 J

10) a. 4.95 m/s b. 0.714 m c. 4.20 m/s

11) 0.657 hp

12) +2.86 m/s

13) +13.0 m/s

14) a. 0.387 m/s b. 1.03 N

15) 908 m/s, 66° S of E

16) 2.93 m

17) a. 3 mm b. 60 Hz c. 2 cm d. 1.2 m/s

18) 324 m/s

19) a. 2190 Hz b. 1840 Hz

20) 350. m/s

21) 2.0 x 10-2 W/m²

22) 194.8 Hz

23) consonance (3/2)

24) 0.166 m

25) a. 139 Hz b. 697 Hz c. there is none

26) a. 128 Hz b. 256 Hz